(adsbygoogle = window.adsbygoogle || []).push({}); The problem statement, all variables and given/known data

Look for a matrix that has row sums 4 and 8, and column sums 2 and x:

matrix =

[a, b] -------I don't know how to do latex

[c, d]

a + b = 4; a + c = 2;

c + d = 8; b + d = s;

The four equations are solvable only if s = ____. Then find two different matrices that have the correct row and column sums. Write down the 4 by 4 system Ax = b with x = (a, b, c, d) and make A triangular by elimination.

Attempt at a solution:

I created a matrix from the system of equations given. I started with:

[1 1 0 0 4]

[0 0 1 1 8]

[1 0 1 0 2]

[0 1 0 1 s]

-->

[1 1 0 0 4]

[0 -1 1 0 -2]

[0 0 1 1 8]

[0 0 1 1 (s-2)]

-->

[1 1 0 0 4]

[0 -1 1 0 -2]

[0 0 1 1 8]

[0 0 0 0 (s-10)]

So I got s = 10.

I can't solve for a, b, c, or d (or can I?)

What am I not understanding and how do I do this problem? Thanks.

edit: Thanks LCKurtz, I got it now.

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# Homework Help: Intro Lin Alg Elimination problem

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